PROVIDENCE, R.I. — Though he refused a firefighters union request to stop the city from continuing a Fire Department work schedule enacted Sunday, a Superior Court judge said Monday that the union was likely to win the argument that the plan's financial effects should be reviewed by an arbitrator.

Firefighters Local 799 and the city went before Associate Justice Jeffrey A. Lanphear to argue two requests by the union. One was for a temporary restraining order stopping the change from four platoons to three and the other asked Lanphear to compel the city to agree that any union damage claims — such as lost overtime from the platoon change — were subject to grievance review and submission to an arbitrator.

The city has estimated that the new system, with more firefighters in each platoon, could mean paying firefighters $5 million less a year in overtime.

Though Lanphear said there was "a real probability that the union will succeed" in court on the arbitration argument, he added that the union's potential losses as the legal process played out weren't dire enough to justify the drastic step of immediate court intervention through a restraining order.

He asked both sides to submit supplemental briefs Tuesday on whether the city could be compelled to agree to arbitration over differences of the effects of the platoon switch. He said he hoped to decide that issue by the end of the week. He also set another hearing for Aug. 12.

The Fire Department switched to the three-platoon system Sunday at 8 a.m. Mayor Jorge O. Elorza has said the three platoons, augmented by the newly assigned former fourth platoon members, will rarely drop below minimum staffing requirements, avoiding millions in overtime and callback pay needed to fill vacancies when shifts in the four-platoon system were understaffed.

But the union complains that the savings are achieved by lengthening the average firefighter's base workweek from 42 to 56 hours and converting what was overtime to straight time.

Union lawyer Edward C. Roy Jr. said he was pleased with Lanphear's remarks. Elorza spokesman Evan England said "the solicitor's office is fully prepared to continue presenting our position on Aug. 12."

Union President Paul Doughty said there was more at stake than just overtime. The plan shortens the workweek scheduling from eight to six days by eliminating two days off. He said that has disrupted some members' daycare arrangements as well as carefully negotiated visitation and custody agreements.

"This is a huge change," he said.

Timothy C. Cavazza, representing the city, argued that a recent state Supreme Court case involving North Kingstown's Fire Department found changing fire department schedules, and the choices made to implement them, were an intrinsic right of management and not subject to the type of arbitration the union sought.

Roy sidestepped some of that argument, conceding that the city had the right to set schedules, but arguing that under the firefighters contract, disagreements over the losses suffered by union members were subject to arbitration.

One of the core issues of the dispute is the status of the firefighters contract. In North Kingstown, the firefighters contract had expired when that platoon change occurred. The Elorza administration claimed in one of its filings in the platoon change matter that the Providence firefighters contract was not properly ratified by the City Council in 2011 and therefore was not valid. The contract contains language dealing with matters subject to arbitration. City Council President Luis Aponte, who was on the council in 2011, has questioned the claim of invalidity.

Roy said the contract also included millions in pension concessions, and if the city claimed it was invalid, then the pension concessions would be invalid as well. He said the union had filed a motion with Superior Court Associate Justice Sarah Tefft-Carter, who oversaw the pension case, to rule on the contract's legitimacy. But he added that a ruling might not be necessary if Lanphear rules the contract is valid and the city doesn't appeal.

Roy said the existence of a contract made the Providence situation "180 degrees different" from North Kingstown. Cavazza disagreed, saying the high court had found the power that the North Kingstown municipal administration was claiming to be so vital to managing the department that it couldn't bargain it away if it wanted to.